Question

Determine whether 4x2 + 6x + 9 is a perfect square. If so, factor it. If not, explain why.
A.No, 4x2 + 6x + 9 is not a perfect square.
4x2 and 9 are perfect squares, but 6x is not equal to 2(2x)(3).
So 4x2 + 6x + 9 is not a perfect square.
B.Yes, 4x2 + 6x + 9 is a perfect square.
(2x + 3)2
C.Yes, 4x2 + 6x + 9 is a perfect square.
(2x − 3)2
D.No, 4x2 + 6x + 9 is not a perfect square.
4x2 and 9 are perfect squares, but 6x is not a perfect square.
So 4x2 + 6x + 9 is not a perfect square.

Answer 1

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Answer:

  A.  No, 4x² + 6x + 9 is not a perfect square. 4x² and 9 are perfect squares, but 6x is not equal to 2(2x)(3).

Step-by-step explanation:

The square of a binomial is ...

  (a +b)² = a² +2ab +b²

Here the first and last terms are perfect squares, so we might assume that ...

  a = 2x, b = 3

This would require the middle term to be 2ab = (2)(2x)(3) = 12x, which it is not. So, the given trinomial is not a perfect square.